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WASHINGTON (CNN) -- A week after the GOP-led Senate rejected an increase to the minimum wage, Senate Democrats on Tuesday vowed to block pay raises for members of Congress until the minimum wage is increased.

"We're going to do anything it takes to stop the congressional pay raise this year, and we're not going to settle for this year alone," Democratic Leader Harry Reid of Nevada said at a Capitol news conference.

"They can play all the games the want," Reid said derisively of the Republicans who control the chamber. "They can deal with gay marriage, estate tax, flag burning, all these issues and avoid issues like the prices of gasoline, sending your kid to college. But we're going to do everything to stop the congressional pay raise."

The minimum wage is $5.15 an hour. Democrats want to raise it to $7.25. During the past nine years, as Democrats have tried unsuccessfully to increase the minimum wage, members of Congress have voted to give themselves pay raises -- technically "cost of living increases" -- totaling $31,600, or more than $15 an hour for a 40-hour week, 52 weeks a year, according to the Congressional Research Service.

In floor debate last week Republicans argued the raise for low-income workers would hurt small businesses. They offered an alternative measure to raise the minimum wage that was tied to tax breaks for small businesses.

The main proposal fell eight votes short of the 60 it needed to pass with 46 opposing; the alternative measure mustered only 45 votes in favor, while 53 senators opposed.

Reid wouldn't spell out the specific tactics he would employ to block the congressional pay raise -- which is triggered each year with the passage of an appropriations bill not by a vote on a stand alone bill to increase pay for members.